How Far Should You Stand from the Statue of Liberty for the Best Viewing Angle?

AI Thread Summary
To determine the optimal viewing distance from the Statue of Liberty for the largest angle, one must consider the height of the statue (46 meters) and its plinth (47 meters). A 2-meter tall observer should analyze various distances within the 66 meters of available land to find the angle of view. The discussion suggests using trigonometric principles, specifically the Law of Sines and the Law of Cosines, to calculate the viewing angle at different distances. Observers are encouraged to experiment with distances such as 1m, 30m, 40m, 50m, and 66m to identify trends in the viewing angle. Ultimately, the goal is to find the distance that maximizes the viewing angle while remaining within the specified limits.
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Homework Statement


The statue of libery is 46 meters tall and stands on a plinth 47 meters tall.
How far back should a 2m tall person stand back to obtain the largest viewing angle? There is 66m of land in front of the statue, will the position be within these 66 meters?
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Homework Equations


Law of Sines: sina/A=sinb/B
Law of cosines: b^2=a^2+c^2-2ac(cosB)

The Attempt at a Solution



I just don't understand what the largest viewing angle will be, wouldn't it just be the closest thing to 180 degrees? Also, wouldn't one theoretically be able to view all of the statue from any distance away?
 
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Easiest way might be to try an answer for few values of distance.
hint - assume the statue and plinth are a straight line.

So if you are 1m from plinth you have a narrow angle between a triangle of base 46m starting 45 away
Then try at 66m and then 30m, 40m, 50m and see what the trend is.

hint, if you haven't done much trig you might want to make it a right angle triangle and then find 'A' by working out the total angle and the angle just below A
 

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